Torque is force with a lever attached
A force pushes. A torque turns. The difference is where the force is applied relative to the pivot, and at what angle.
Three things raise the torque: a bigger force, a longer lever arm, and an angle closer to 90°. Only the first is obvious, and the third is the one people get wrong.
Only the perpendicular part counts
Push on a wrench at right angles and every newton contributes. Push at a shallow angle and most of your effort goes into pulling the wrench along its own length, where it achieves nothing. That is what the sine does in the formula: it strips out the wasted component.
| Angle | sinθ | Torque |
|---|---|---|
| 90° | 1.00 | 15.0 N·m |
| 60° | 0.87 | 13.0 N·m |
| 30° | 0.50 | 7.5 N·m |
| 0° | 0.00 | 0 N·m |
The last row is the useful one to sit with. Pushing directly along the lever, however hard, turns nothing at all.
Where it shows up
Tightening a bolt to spec, sizing a motor, working out whether a longer wrench will free a seized nut, or understanding why an engine's torque figure tells you about pulling power while its horsepower tells you about speed. Same formula behind all of them.
Frequently asked questions
What is the torque formula?
τ = r · F · sin θ, where F is the force, r is the distance from the pivot to where the force is applied, and θ is the angle between the force and the lever arm. With 50 N at 0.3 m and 90°, that is 50 × 0.3 × 1 = 15 N·m.
Why does the angle matter so much?
Because only the component of the force at right angles to the lever does any turning. At 90° all of it counts. At 30° only half does, so the same 50 N at 0.3 m gives 7.5 N·m instead of 15. Push straight along the lever, at 0°, and you get no torque at all no matter how hard you push.
How do I convert N·m to lb·ft?
Multiply by 0.7376. So 15 N·m is 11.06 lb·ft. Going the other way, multiply pound-feet by 1.356. The calculator shows both at once so you do not have to.
What is the difference between torque and power?
Torque is turning force at an instant; power is how fast work gets done, which is torque times rotational speed. An engine can make large torque at low revs and modest power, which is why tractors and sports cars feel so different despite similar power figures.
Why is a longer wrench easier?
Because torque scales with distance from the pivot. Double the wrench length and the same hand force gives double the torque. That is the whole reason breaker bars exist, and why the calculator treats r as a lever rather than just a number.